Bring a large pot of water to a boil over high heat. Slowly lower the eggs into the boiling water. Reduce heat to a rolling simmer. Cook for 12-13 minutes.
While the eggs are cooking, set up a bowl of ice water. Once the eggs are finished cooking, remove them from the hot water with a slotted spoon and place them into the ice bath for 5-10 minutes.
Peel and chop the eggs. Set aside.
Cook the Potatoes
Place potatoes in a large pot and cover with water. Cover the pot. Bring to a boil and cook for 20 minutes.
Drain and potatoes and rinse with cold water. Peel the skins off and cut into bite sized pieces.
Make the Potato Salad
Dice the celery. Grate the onion.
In a large bowl, combine the mayonnaise, mustards, hot sauce, grated onion, relishes, salt and pepper. Whisk until smooth.
Fold the potatoes, eggs and celery into the mayonnaise mixture. Serve at room temperature.
Keyword gluten free, potatoes, side dish, vegetarian